B14-isra04sa - Shape Restoration by Active Self-Assembly...

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Shape Restoration by Active Self-Assembly Daniel Arbuckle and Aristides A. G. Requicha Laboratory for Molecular Robotics University of Southern California Los Angeles, California, USA {daniel.arbuckle | requicha} @ usc.edu Abstract - Shape restoration is defined as the problem of constructing a desired, or goal, solid shape Sg by growing an initial solid Si which is a subset of the goal but is otherwise unknown. This definition attempts to capture abstractly a situation that often arises in the physical world when a solid object loses its desired shape due to wear and tear, corrosion or other phenomena. For example, if the top of the femur becomes distorted, the hip joint no longer functions properly and may have to be replaced surgically. Growing it in place back to its original shape would be an attractive alternative to replacement. This paper presents a solution to the shape restoration problem by using autonomous assembly agents (robots) that self-assemble to fill the volume between Sg and Si. If the robots have very small dimensions (micro or nano), the desired shape is approximated with high accuracy. The assembly agents initially execute a random walk. When two robots meet they may exchange a small number of messages. The robot behavior is controlled by a finite state machine with a small number of states. Communication on contact models chemical communication, which is likely to be the medium of choice for robots at the nanoscale, while small state and small messages are limitations that also are expected of nanorobots. Simulations presented here show that swarms of such robots organize themselves to achieve shape restoration by using distributed algorithms. This is one more example of an interesting geometric problem that can be solved by the active self-assembly paradigm introduced in previous papers by the authors. Index Terms – self-assembly; swarm robotics. I. INTRODUCTION This paper is concerned with active assembly agents whose capabilities include a limited ability to exchange information with neighbors, to grip, release and move relative to neighbors, to perform a random walk through their environment, and to decrement a number. This small set of actions, controlled by a finite state machine, are sufficient to allow the solution of a large class of tasks through self- assembly. We have previously explored some of the capabilities of such assembly agents in [1]. In this paper, we address the problem of self-assembling a goal shape around a pre-existing object of unknown shape. We use Active Self-Assembly to achieve this goal. The paper begins with a description of some related work, followed by a description of what we are trying to achieve and the general approach we have taken. Following this are three sections describing our methods in more detail. Finally we discuss the results of applying these techniques in
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This note was uploaded on 07/22/2008 for the course CS 549 taught by Professor Requicha during the Spring '08 term at USC.

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B14-isra04sa - Shape Restoration by Active Self-Assembly...

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